How to let Mesh Deform modifier work as expected
For very rough cage, especially when using larger cage to control smaller target mesh, you need to set a higher value for Precision.

So, two ways to solve this:


Try to scale down the cage object;
Try to set a higher Precision value in the Mesh Deform modifier panel. (5 might be relatively appropriate for this particular case)


Note:


Normals on cage mesh are used to determine the inside/outside of the cage, so make sure they are pointing outside. Flip them if not.
The cage mesh has to be a closed mesh (manifold) to work well. When in Vertex or Edge selction mode, You can press ShiftCtrlAltM to find the non-manifold edges.